HOW STABLE ARE INSTRUMENTAL BIASES P2-C2?

. . This paper presented results of investigations about estimation DCB P2-C2 for satellites and receiver in GPS system. The data from LAMA station in Poland were used to determination of stability instrumental biases P2-C2, using least square method. Author proposed new strategy to solution of DCB P2-C2 (biases were calculated with temporal resolution 2 hours). The test results were compared with CODE’s product. Difference between proposed method and CODE’s values for Satellite DCB is less than ± 1 ns and for Receiver DCB less than ± 0.2 ns. Standard deviation of presented method is about 0.4 ns.


Introduction
Starting from 2005, when USA launched satellite PRN17, users on the all world could received new civil signal C2 at the 2 nd frequency in GPS system. At first only three satellites: PRN12, PRN17, PRN31 and currently twelve satellites: PRN1, PRN5, PRN7, PRN12, PRN15, PRN17, PRN24, PRN25, PRN27, PRN29, PRN30 and PRN31, are able to transmitted new signal L2C. These group of satellites is called Block IIR-M, where "R" means replenishment and "M" means modernized [5].
New signal L2C was the reason to create special applications, which can determine relation between code P2 and code C2.
In GPS system, this relation is called Differential Code Biases P2-C2, but in numerical computations many users separate DCB P2-C2 on two types: Satellite DCB P2-C2 and Receiver DCB P2-C2. Instrumental biases SDCB P2-C2 are called difference of transmission time between observations P2 and C2 from each satellite to receiver. Instrumental biases RDCB P2-C2 are called difference of travel time between observations P2 and C2 from antenna to hardware of receiver [2]. Magnitude of values DCB P2-C2 is about ± 1 ns (nearly ± 30 cm).
Only few organizations or scientific institutions from all over the world estimate instrumental biases P2-C2, for example: the Center for Orbit Determination in Europe (CODE), the Natural Resources Canada (NRCan), the University of New Brunswick (UNB). CODE and NRCan determinate DCB P2-C2 using Geometry Free combination based on collections data from global network from all day [1,4,6]. UNB calibrate Satellites DCB P2-C2 in GAPS software using Ionosphere-Free linear combination (also based on collections data from global network from all day) [3,5].
Author in article presents new strategy to estimation DCB P2-C2 using observations data from single station. Code source of program "SciTEC" was written in Scilab 5.4.1 language. Description of mathematical model is located in section "Estimation DCB P2-C2". Results of calculations will be found in section "Experiment and Result", and last part of article has got some conclusions.

Estimation DCB P2-C2
To determine instrumental biases P2-C2 Geometry Free linear combination is used, free from geometric errors, troposphere and ionosphere delay, satellite and receiver clock errors. Basic equation for P2 and C2 observation is given by: where: geometric distance between satellite and receiver, cspeed of light, , os ttreceiver and satellite clock error, 2 Iionosphere delay at the 2 nd frequency, Ttroposphere delay, , SDCB RDCBinstrumental biases for satellites and receivers. Subtracting equation (2) from (1), geometric errors and systematic errors are eliminated, as follows: DCB P2-C2 from equation (3) are estimated using least square method: where: xvector with unknown biases; Amatrix with dimension (n, m); matrix has got rank deficient, which equals one; lvector of observations. Rank deficient is reduced if one constraint is added to matrix A . Typical constraint-reference sum of Satellite DCB P2-C2 equals zero, is applied as follows: where nnumber of satellites. Based on equation (5), satellites biases are stable relative to centre of gravity frame of all SDCB P2-C2. Another constraint can be also utilized, e. g. one bias of SDCB P2-C2 is known as a prori value. In this procedure all unknown biases are obtained in relation to reference bias, so very major is determinated mean error of reference bias.
Mean errors for unknown biases are estimated using equation

Experiment and Results
In analysis were used 24 hours (with interval 30 seconds) GPS data from LAMA station in RINEX format 2.11. LAMA reference station is located in north-eastern Poland (coordinate: 53.71 N, 20.67 E). Station has got dual frequency receiver LEICA GRX1200+GNSS, which can register code observations: C1, P2, C2 and phase observations: L1, L2. Collections of RINEX data were downloaded from BKG server: [8]. Calculations were executed in "SciTEC" software in temporal resolution 2 hours. "SciTEC" is open source toolbox, which code source was written in Scilab 5.4.1 numerical platform. After 24 hours, results from each sessions were saved and next mean value and standard deviation were calculated. Final results were compared with CODE's DCB P2-C2 monthly product (from website [9]). In Table 1 is presented results from day 083 to 086, 2014 year, as a examples of proposed strategy.
Aspect of stability instrumental biases is very important in submitted paper. After 4 days of investigations, for individual satellite and receiver, were computed daily repeatability of DCB P2-C2 (see Table 2). Magnitude of daily repeatability, for SDCB P2-C2, is between 0.04  0.19 ns. More than 0.1 ns have got four satellites: PRN5, PRN12, PRN17, PRN25, but for rest satellites daily repeatability is below 0.07 ns. In case of RDCB P2-C2, daily repeatability is less than 0.06 ns (about 2 cm), and it can be concluded that instrumental biases P2-C2 are very stable. Average value of SDCB P2-C2 over 4 days can reach up to 0.822 ns (maximum result) and -0.769 ns (minimum result). Difference between maximum and minimum value is more than 1.5 ns (about 45 cm). Among all results of SDCB P2-C2, more than 54% are negative and only 5 values are positive.

Conclusions
In this paper, new strategy of estimation instrumental biases P2-C2, were showed. The test results of proposed method were compared with monthly CODE's product. Difference between presented method and global solution is less than ± 1 ns, with standard deviation about 0.4 ns. Additionally, aspect of stability DCB P2-C2, were described in article. Daily repeatability of SDCB P2-C2 is less than 0.19 ns and for RDCB P2-C2 about 0.06 ns. In future, code source of program will be usable in determination IFB P2-C2 in GLONASS system.